Since the beginning of the COVID-19 spreading, the number of studies on the epidemic models increased dramatically. It is important for policymakers to know how the disease will spread and what are the effects of the policies and environment on the spreading. In this paper, we propose two extensions to the standard SIR model: (a) we consider the prevention measures adopted based on the current severity of the infection. Those measures are adaptive and change over time; (b) multiple cities and regions are considered, with population movements between those cities and regions, while taking into account that each region may have different prevention measures. Although the adaptive measures and mobility of the population were often observed during the pandemic, these effects are rarely explicitly modeled and studied in the classical epidemic models. The model we propose gives rise to a plateau phenomenon: the number of people infected by the disease stays at the same level during an extended period of time. We show what are conditions need to be met in order for the spreading to exhibit a plateau period in a single city. In addition, this phenomenon is interdependent when considering multiple cities. We verify from the real-world data that the plateau phenomenon does exist in many regions of the world in the current COVID-19 development. Finally, we provide theoretical analysis on the plateau phenomenon for the single-city model and derive a series of results on the emergence and the ending of the plateau, as well as on the height and length of the plateau. Our theoretical results match well with our experimental findings.